Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials


Swamy S. R. , Yalçın Tokgöz S.

Problemy Analiza-Issues of Analysis, vol.11, no.29-1, pp.133-144, 2022 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 29-1
  • Publication Date: 2022
  • Doi Number: 10.15393/j3.art.2022.10351
  • Title of Journal : Problemy Analiza-Issues of Analysis
  • Page Numbers: pp.133-144
  • Keywords: Fekete-Szego functional, regular function, bi-univalent function, Gegenbauer polynomials

Abstract

The main goal of the paper is to initiate and explore two sets of regular and bi-univalent (or bi-Schlicht) functions in D = {z is an element of C : vertical bar z vertical bar < 1} linked with Gegenbauer polynomials. We investigate certain coefficient bounds for functions in these families. Continuing the study on the initial coefficients of these families, we obtain the functional of Fekete-Szego for each of the two families. Furthermore, we present few interesting observations of the results investigated.